Problem: Simplify the following expression: $p = \dfrac{-7k^2 - 14k + 21}{k - 1} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ p =\dfrac{-7(k^2 + 2k - 3)}{k - 1} $ Then we factor the remaining polynomial: $k^2 + {2}k {-3} $ ${-1} + {3} = {2}$ ${-1} \times {3} = {-3}$ $ (k {-1}) (k + {3}) $ This gives us a factored expression: $\dfrac{-7(k {-1}) (k + {3})}{k - 1}$ We can divide the numerator and denominator by $(k + 1)$ on condition that $k \neq 1$ Therefore $p = -7(k + 3); k \neq 1$